One such alternative measure is statistical rate fairness [1]} when the probability distribution domain can be further split in to include target class \( Y \in \mathcal {Y} \) . The statistical rate fairness constraint can be expressed by replacing the marginal distributions in Eq. (REF ) with conditional \( p[Y = y \mid A = a] \) , where \(y \in \mathcal {Y}\)  is fixed beforehand:
\(\frac{p[Y = y \mid A = a_{i}]}{p[Y = y \mid A = a_{j}]} \ge \rho ,\) 
